Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates

TL;DR

This paper investigates the stability and dynamics of a single vortex ring in anisotropic three-dimensional Bose-Einstein condensates, combining theoretical analysis with numerical simulations of the Gross-Pitaevskii equation.

Contribution

It provides a comprehensive analysis of vortex ring stability in anisotropic traps, extending previous work by including nonlinear dynamics and finite chemical potential effects.

Findings

Vortex ring stability is predicted for 1 ≤ λ ≤ 2.

Numerical simulations show the stability interval narrows at finite chemical potential.

Good agreement between theoretical predictions and GPE simulations for vortex dynamics.

Abstract

In the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing the evolution of a vortex ring and not only consider its spectrum of linearized excitations, but also explore the full nonlinear dynamical evolution of the ring as a vortical filament. The theory predicts that the ring is stable for $1 \leq \lambda \leq 2$, where $\lambda=\omega_z/\omega_r$ is the ratio of the trapping frequencies along the $z$ and $r$ axes, i.e., for spherical to slightly oblate condensates. We compare this prediction with direct numerical simulations of the full 3D Gross-Pitaevskii equation (GPE) capturing the linearization spectrum of the ring for different values of the chemical potential and as a function of the anisotropy parameter $\lambda$. We identify this result as being only asymptotically valid as the chemical potential $\mu \rightarrow \infty$, revealing how the stability interval narrows and, in particular, its upper bound decreases for finite $\mu$. Finally, we compare at the dynamical level the results of the GPE with the ones effectively capturing the ring dynamics, revealing the unstable evolution for different values of $\lambda$, as well as the good agreement between the two.